Question : What is the total surface area of a pyramid whose base is a square with a side 8 cm and the height of the pyramid is 3 cm?
Option 1: 169 cm2
Option 2: 121 cm2
Option 3: 144 cm2
Option 4: 184 cm2
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Correct Answer: 144 cm 2
Solution :
Given,
The side of the square base = 8 cm and the height of the pyramid = 3 cm
The slant height (l) of the pyramid needs to be evaluated,
⇒ l
2
= ($\frac{\text{side}}{2}$)
2
+ (Height)
2
⇒ l
2
= 4
2
+ 3
2
⇒ l
2
= 16 + 9
⇒ l
2
= 25
⇒ l = 5 cm
The total surface area of the pyramid
= (Base Area) + $\frac12$ × (Perimeter of base) × (Slant height)
= 64 + $\frac12$ × 32 × 5
= 64 + 16 × 5
= 64 + 80
= 144 cm
2
Hence, the correct answer is 144 cm
2
.
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